The trapping problem on horizontal partitioned level-3 sierpinski gasket networks

Abstract

Random walk on complex networks is a research hotspot nowadays. The average trapping time (ATT) is an important property related to the trapping problem, which is a variant of random walk, because it can be used to measure the transmission efficiency of particles randomly walking on the network. In this paper, we consider the trapping problem on the horizontal partitioned level-3 Sierpinski gasket network which is determined by the cutting line lk, that is, by the partition coefficient k. Then through the structure of this research model, we derive the exact analytical expression of the ATT. Furthermore, we draw two kinds of numerical simulation diagrams to simulate the relationship between the ATT and the iteration number and the partition coefficient, and compare them with the ATT on the original graph (uncut). The obtained solution shows that the ATT is affected by the k, specifically, the larger the k, the shorter the ATT, that is the higher the transmission efficiency.

Average trapping time on horizontally divided 3-dimensional 3-level Sierpinski gasket network

“…Wu Bo et al [14,15] studied the average trapping time on a network of half-Sierpinski gasket and twodimensional three-level Sierpinski gasket. Zhongren Hu et al [16] studied the average trapping time on a twodimensional horizontally segmented Sierpinski gasket network. Qi Yi et al [17] obtained several expressions for the hit time of random wandering on Sierpinski and hierarchical graph.…”